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  3. Physics
  4. The pressure P and volume V of a gas are related as PV3/2 = K, where K is a constant. The percentage increase in the pressure for a diminution of 0.5 % of the volume is

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Q. The pressure $P$ and volume $V$ of a gas are related as $PV^{3/2} = K$, where $K$ is a constant. The percentage increase in the pressure for a diminution of $0.5\%$ of the volume is

Physical World, Units and Measurements

Solution:

As $P\,\propto\,V^{3/2} \Rightarrow \frac{\Delta P}{P}=-\frac{3}{2} \frac{\Delta V}{V}$. Therefore, percentage increase in pressure $=\frac{3}{2}\times0.5=0.75\%$